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The MIT Blackjack Team's Story

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The MIT Blackjack Team's Story Twenty-One The casino game of Twenty-One, popularly called Blackjack (actually the home version of the game), achieved wider popularity when computers showed in the early 60s that the game could be beaten. Players flocked to Las Vegas and Reno, thinking to win scads of money, but the great majority did not have the skills and discipline needed to win. The casinos loved the extra business. The film "21," based on the book by Ben Mezrich entitled "21: Bringing Down the House," screen play by Peter Seinfeld and Allan Loeb, tells the story of a group of students from the Massachusetts Institute of Technology (MIT), who in 1994 formed a team of players with the initial goal of beating the game in Las Vegas casinos. The film’s hero was named Ben, the book’s was Kevin. This was not a new idea, as professional player Ken Uston had done the same a decade before. The MIT team merely copied his tactics, with minor variations. Before going further, let's look first at a 21 table and typical rules for its game: Four or more half-moon shaped 21 tables are arrayed in a circle, with dealers behind each table facing the outer rounded side and its five to seven player seats. A plastic card shows the rules in effect, including minimum and maximum bets. There may be many large table groups. The tables enclose a "pit" area in which pit personnel, one of whom is the "pit boss," monitor the tables, with telephones and a computer display on hand. The dealer handles the cards, converts players' cash into chips, pays out wins and collects losses. The game begins with a shuffle of the cards (standard decks) by the dealer and a cut by one of the players. A player bets by putting one or more chips into the circle in front of him. Playing multiple circles is allowed if one or more adjacent circles are available. The dealer gives each player two cards for a "hand," plus two for himself, the second face up on top of a face-down "hole card." The cards are ranked A, 2, 3, ...9, 10, Jack, Queen, King, with the ace having a value of either 1 or 11 (as desired during play) and face cards count as 10, so we call them 10s. The goal is to have a total as close as possible, or equal to, 21. If the total is greater than 21, the player loses ("busting"), even if the dealer busts too. Players with a low total can ask for additional cards ("hits"), one at a time, until they are satisfied ("standing") or they bust. They have the option of doubling their bet and taking just one card (a "double down"). A hand with a pair (10-cards need not be identical) can be split to make two hands, with an additional card added to each. These are then played normally. Some tables permit doubling down after splitting, some don't. If a split card is dealt a card of the same value, a "resplit" is allowed up to as many as four hands, but a pair of aces may be split only once and each gets only one card. If a player's two original cards are an ace and a 10, that is a "natural," popularly called a Blackjack. Instead of getting even money he gets 1-1/2 times the bet unless the dealer has a natural also, in which case he ties. Other than that a dealer's natural means all players lose, even those with a non-Blackjack total of 21. When the dealer's up-card is an ace, players are offered a side bet (called "Insurance") on whether the down card will give the dealer a natural. They can place up to 1/2 their original bet to take that wager, which pays 2 to 1 if successful. When all players have played their hands in turn, the dealer plays his. He must hit if his total is less than 17 and must stand on 17 or more. The table rules may require the dealer to hit a "soft" 17 like A,6 (which is advantageous to the house). A soft hand is one that can count an ace as either 1 or 11. Players win (even money), tie, or lose their bet depending on whether their total exceeds, ties, or is less than the dealer's total. If the dealer busts, those who have not busted are winners with any total. A thorough discussion of the rules can be seen at www.blackjackinfo.com, "The World's Most Popular Blackjack Website." Three skills are required for winning at 21: (1) evaluating the favorability of the remaining cards and betting accordingly, (2) playing hands accurately, and (3) doing (1) and (2) without arousing suspicion of doing them well. In Nevada, a casino can legally bar a player from the game if his skill seems excessive. Skill (3) requires "camouflage," looking and acting like a typical stupid gambler who is destined to be a loser. Using whiskey as a "deodorant" earlier is helpful. Evaluating Favorability ("Counting") The MIT team strategy was used against games having four or more decks dealt out of "shoes," not the single or double-deck games in which cards are hand-dealt. While the odds slightly favor the casino at the beginning of dealing, as cards are dealt the odds fluctuate between favorable and unfavorable to the player. Tens and aces are good for the player (e.g., more naturals and successful double downs), while small cards are bad (the dealer is less likely to bust). Recognizing when the remaining cards favor the player is the aim of "counting." The book refers to their use of "a highly technical count" to evaluate favorability. Well, the count they used is the very simple Hi-Lo, with cards 2 through 6 counted as +1, ace and 10s as -1. It is a count suggested for beginners, not as accurate as some others. A so-called "counter" using Hi-Lo merely maintains a running count of the number of low cards seen, while subtracting the number of aces and 10s When the total is positive, the remaining cards are favorable to the player. How favorable? The count derived during play is called the "running count," with must be adjusted to make it a "true count." This means dividing the count by the number of decks remaining. A running count of +18 is a true count of +9 if two decks remain undealt. The rule of thumb is that each positive true count represents a player advantage of 1/2 of one percent. Since a shoe is typically that unfavorable to begin with, the true count must be reduced by one before judging the current favorability. A true count of +9 becomes +8, which multiplied by .005 is .04, which means a 4 % advantage for the player. Bet Sizing Obviously the size of a bet should be related to both the favorability of the wager and the available bankroll. If you bet too much when the odds are in your favor, you can endanger your bankroll; bet too little, and you miss out on some good profits. It therefore is logical to practice "fractional betting," wagering fractions of bankroll based on the favorability of the bet. A popular principle for sizing bets in favorable situations is known as "Optimal Betting" (OB), aka the "Kelly Criterion," named after J. L. Kelly Jr, who published it in The Bell System Technical Journal in 1956. Its goal is to maximize the probable growth rate of bankroll. This is equivalent to having a logarithmic utility function, as the probability of losing half of the bankroll is the same as for doubling it, an attractive balancing of moderate risk with large potential gain. If that seems too risky, betting a smaller fraction reduces the chance of losing half the bankroll, while increasing the time required to double it. Many find that more comfortable. OB is explained in detail on my web site, under "Blackjack Topics." If a wager is simple win-loss, the OB bet size is a fraction of current bankroll that equals a bet's mathematical advantage ("edge"). When flipping a coin biased 51-49 (2% edge) in favor of heads, the OB for heads is 2% of the current bankroll for each flip. Those who would bet 4% could make a lot more money, but the most likely outcome is that their bankroll would be unchanged in the long run (after large swings of fortune). Those who would bet an even larger percentage are most likely to end up losers in the long run, and the swings will be even more extreme. If the possible results of a bet have a wide variance, as with a complex game like 21 (which can have multiple payoffs or payouts per hand that exceed the original bet size), the advantage must be divided by the variance (standard deviation squared) of the results to determine OB. The variance of 21 depends on the rules in force, including the number of decks, but is typically between 1.2 and 1.3, let's say 1.25. When the advantage is .04, that must be divided by 1.25 to get the right fraction for betting, which is .032 (3.2% of bankroll). Since each positive Hi-Lo true count (after subtracting one for the house) represents approximately a 0.5% advantage, we can say that OB dictates a bet size of .005 / 1.25 of bankroll x (true count -1).
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